Carbon has numerous one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) allotropic structures. The study of carbon materials has been a major focus of material science and condensed matter physics. Previous studies have identified different classes of topological semimetallic carbon allotropes with different topological phases. In this review, we first give a brief summary of the development of carbon allotropes from 1D to 3D. Next, we discuss topological properties of carbon materials and their physical origin. Then, we consider possible expansion of the topological study of carbon materials to other light-element materials such as boron. Finally, we present future prospects in pursue of topological physics within carbon allotropes.
Raman spectroscopy has been used in chemistry and physics to investigate the fundamental process involving light and phonons (quantum of lattice vibration). The carbon nanohorn introduces a new subject to Raman spectroscopy, namely topology. We show theoretically that a photo-excited carrier with a non-zero winding number activates a topological $D$ Raman band through the Aharonov-Bohm effect. The topology-induced $D$ Raman band can be distinguished from the ordinary $D$ Raman band for a graphene edge by its peak position.
Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted b…
The topological phase transition is theoretically studied in a metallic single-wall carbon nanotube (SWNT) by applying a magnetic field $B$ parallel to the tube. The $\mathbb{Z}$ topological invariant, winding number, is changed discontinuously when a small band gap is closed at a critical value of $B$, which can be observed as a change in the number of edge states owing to the bulk-edge correspondence. This is confirmed by numerical calculations for finite SWNTs of $\sim$ 1 $μ$m length, using a one-dimensional lattice model to effectively describe the mixing between $σ$ and $π$ orbitals and s…
The rapid outbreaks of lethal viruses necessitate the development of novel antiviral substance. Besides the conventional antiviral substances, biocompatible nanomaterials also have significant potential in combating the virus at various stages of infection. Carbon nanomaterials have an impressive record against viruses and can deal with many crucial healthcare issues. In accordance with the published literature, biocompatible carbon nanomaterials have a promising prospect as an antiviral substance. Subsequently, the antiviral properties of different carbon nanomaterials namely fullerene, carbo…
A structurally stable carbon allotrope with plentiful topological properties is predicted by means of first-principles calculations. This novel carbon allotrope possesses the simple space group C2/m, and contains simultaneously sp, sp2 and sp3 hybridized bonds in one structure, which is thus coined as carboneyane. The calculations on geometrical, vibrational, and electronic properties reveal that carboneyane, with good ductility and a much lower density 1.43 g/cm3, is a topological metal with a pair of nodal lines traversing the whole Brillouin zone, such that they can only be annihilated in a…
The topological metal states in electronic systems have been extensively studied, but topological phonons were explored only in few examples so far. Here, we expose for the first time that the topological nodal gimbal phonons, type-I and type-II Weyl phonons are simultaneously present in T-carbon, a recently realized new allotrope of carbon. At about 15.2 THz, we find that there exist three mutually intersecting nodal loops (named as nodal gimbal phonons) around Γ point, and two pairs of type-I Weyl phonons on the boundary of Brillouin zone around each X point. In addition, there exist three p…
In this work, we propose a new methodology for obtaining 3D carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and 'slice' it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the Tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of obtained 2D 'sliced' structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC along different directions can generate not only the target Tubu…
The vibrational modes of some single wall carbon nanotube (SWNT) intramolecular junctions (IMJs) have been calculated using the newest Brenner reactive empirical bond order (REBO) potential, based upon which their nonresonant Raman spectra have been further calculated using the empirical bond polarizability model. It is found that the Raman peaks induced by pentagon defects lie out of the $G$-band of the SWNTs, so the high-frequency part of the Raman spectra of the SWNT IMJs can be used to determine experimentally their detailed geometrical structures. Also, the intensity of the Raman spectra …
A two-step doping process, magnetic followed by charge or vice versa, is required to produce insulating massive surface states in topological insulators for many physics and device applications. Using first-principles calculations, we demonstrate here simultaneous magnetic and hole doping achieved with a single dopant, carbon, in Bi2Se3. Carbon substitution for Se (CSe) results in an opening of a sizable surface Dirac gap (53-85 meV), while the Fermi level (EF) remains inside the bulk gap and close to the Dirac point at moderate doping concentrations. The strong localization of 2p states of CS…
Quasi-continuous structural transformation from the crystalline to amorphous state takes place in graphite during ball-milling. The quantitative characteristics of a short- and a medium-range orders in carbon nanomaterials structure are determined by a combined application of X-ray diffraction analysis, reverse Monte Carlo modeling and Voronoi diagram method. High resolution TEM images revealed formation of globular carbon materials having onion-like structure. The Voronoi polyhedra (VP) constructed for simulated atomic configurations of the ball-milled graphite have an extraordinary variety i…
Efforts aimed at large-scale integration of nanoelectronic devices that exploit the superior electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) remain limited by the difficulties associated with manipulation and packaging of individual SWNTs. Alternative approaches based on ultra-thin carbon nanotube networks (CNNs) have enjoyed success of late with the realization of several scalable device applications. However, precise control over the network electronic transport is challenging due to i) an often uncontrollable interplay between network coverage and its topolog…
Topological nodal rings can be classified into three types according to the slopes in their energy dispersion. The first two are made of type-I and II nodal points, respectively, while the third is made of both. In carbon networks, all three types can exist. Under strain, phase transitions from a topological metal to a semiconductor, take place, and at the transition points, these nodal rings shrink into type-I, II, and III semi-Dirac points. These topological features exhibit diverse electron-hole pocket patterns and Landau levels, which give rise to exotic transport properties.
CARBON-2D Topological Descriptor (C2DTD): An Interpretable and Physics-Informed Representation for Two-Dimensional Carbon Networks
Federal University of Paraná（巴拉那联邦大学）；Interdisciplinary Center for Science, Technology, and Innovation, Federal University of Paraná（巴拉那联邦大学跨学科科学与技术创新中心）；College of Technology, University of Brasília（巴西利亚大学技术学院）；State University of Ponta Grossa（蓬塔格罗萨州立大学）；Institute of Physics, University of Brasília（巴西利亚大学物理研究所）
3D carbon allotropes: Topological quantum materials with obstructed atomic insulating phases, multiple bulk-boundary correspondences, and real topology
The exploration of topological phases in carbon allotropes offers a fascinating avenue to realize topological devices based on carbon materials. Here, using first-principles calculations, we propose a novel metastable carbon allotrope, which possesses exotically helical carbon chains bridged by quadrangle-rings. This unique structure with sp2-sp3 bonding networks crystallizes in a noncentrosymmetric face-centered orthogonal (fco) lattice with six atoms in a unit cell, thus named fco-C6. The considerable stability of fco-C6 is confirmed by phonon spectra, elastic constants, and ab initio molecu…
The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we…
The recent progress in the field of hydrogen storage in carbon and boron nitride nanostructures has been summarized. Carbon and boron nitride nanostructures are considered advantageous in this prospect due to their lightweight and high surface area. Demerits of pristine structures to hold hydrogen molecules for mobile applications have been highlighted by many researchers. In such cases, weak van der Waals interaction comes into account, hence, the hydrogen molecules are weakly bonded with the host materials and hence weak adsorption energy and low hydrogen molecules uptake. So, to tune the ad…
Nexus metals represent a new type of topological material in which nodal lines merge at nexus points. Here, we propose novel networks in nexus systems through intertwining between nexus fermions and additional nodal lines. These nexus networks can be realized in several recently synthesized carbon honeycomb materials. In these carbon honeycombs, we demonstrate a phase transition between a nexus network and a system with triply-degenerate points and additional nodal lines. The Landau level spectra show unusual magnetic transport properties in the nexus networks. Our results pave the way toward …
Topological insulators are new quantum states with helical gapless edge or surface states inside the bulk band gap.These topological surface states are robust against the weak time-reversal invariant perturbations, such as lattice distortions and non-magnetic impurities. Recently a variety of topological insulators have been predicted by theories, and observed by experiments. First-principles calculations have been widely used to predict topological insulators with great success. In this review, we summarize the current progress in this field from the perspective of first-principles calculatio…
A series of carbon allotropes with novel optoelectronic and rich topological properties is predicted by systematic first-principles calculations. These fascinating carbon allotropes can be derived by inserting acetylenic linkages (-C$\equiv$C-) into graphite, hence they are termed as grapheaynes. Grapheaynes possess two different space groups, $P$2/$m$ or $C$2/$m$, and contain simultaneously the $sp$, $sp^2$, and $sp^3$ chemical bonds. They have formation energies lower than the already experimentally synthesized graphdiyne and other theoretically predicted carbon allotropes with acetylenic li…
Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative curvature, called Mackay-Terrones crystals (MTC), have been proposed and experimentally explored, yet their topological properties remain to be discovered. Based on the first-principle calculations, we report an all-carbon MTC with topologically non-trivial electronic states by exhibiting node-lines in bulk. When the node-lines are projected on to surfaces to fo…
Carbon, the basic building block of our universe, enjoys a vast number of allotropic structures. Owing to its bonding characteristic, most carbon allotropes possess the motif of hexagonal rings. Here, with first-principles calculations, we discover a new metastable three-dimensional carbon allotrope entirely composed of pentagon rings. The unique structure of this "Pentagon Carbon" leads to extraordinary electronic properties, making it a cornucopia of emergent topological fermions. Under lattice strain, Pentagon Carbon exhibits topological phase transitions, generating a series of novel quasi…
Carbon, a basic versatile element in our universe, exhibits rich varieties of allotropic phases, most of which possess promising nontrivial topological fermions. In this work, we identify a distinct topological phonon phase in a realistic carbon allotrope with a body-centered cubic structure, termed bcc-C$_{8}$. We show by symmetry arguments and effective model analysis that there are three intersecting phonon nodal rings perpendicular to each other in different planes. The intersecting phonon nodal rings are protected by time-reversal and inversion symmetries, which quantize the corresponding…
Here we present an overview of recent fundamental studies on the nature of the interaction between individual metal atoms and metal clusters and the conjugated surfaces of graphene and carbon nanotube with a particular focus on the electronic structure and chemical bonding at the metal-graphene interface. We discuss the relevance of organometallic complexes of graphitic materials to the development of a fundamental understanding of these interactions and their application in atomtronics as atomic interconnects, high mobility organometallic transistor devices, high-frequency electronic devices,…
Carbon is one of the most intriguing elements in the Periodic Table. It forms many allotropes, some being known from ancient times (diamond and graphite) and some discovered ten to twenty years ago (fullerenes, nanotubes). Quite interestingly, the two-dimensional form (graphene) has been obtained only very recently, and immediately attracted great deal of attention. Electrons in graphene, obeying linear dispersion relation, behave like massless relativistic particles, which results in a number of very peculiar electronic properties observed in this first two-dimensional material: from an anoma…
We propose the concept of 2D non-Abelian topological insulator which can explain the energy distributions of the edge states and corner states in systems with parity-time symmetry. From the viewpoint of non-Abelian band topology, we establish the constraints on the 2D Zak phase and polarization. We demonstrate that the corner states in some 2D systems can be explained as the boundary mode of the 1D edge states arising from the multi-band non-Abelian topology of the system. We also propose the use of off-diagonal Berry phase as complementary information to assist the prediction of edge states i…
Using evolutionary algorithm for crystal structure prediction, we present a new stable two-dimensional (2D) carbon allotrope composed of polymerized as-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy is lower than most of the reported 2D allotropes of graphene. Crucially, the crystal structure realizes a nonsymmorphic layer group that enforces a nontrivial global topology of the band structure with two Dirac cones lying perfectly at the Fermi level. The absence of electron/hole pockets makes PAI-graphene a pristine crystalline topological semimetal having anisotropic Ferm…
We report a general scheme to systematically construct two classes of structural families of superhard sp3 carbon allotropes of cold compressed graphite through the topological analysis of odd 5+7 or even 4+8 membered carbon rings stemmed from the stacking of zigzag and armchair chains. Our results show that the previously proposed M, bct-C4, W and Z allotropes belong to our currently proposed families and that depending on the topological arrangement of the native carbon rings numerous other members are found that can help us understand the structural phase transformation of cold-compressed g…
Designing new 2D systems with tunable properties is an important subject for science and technology. Starting from graphene, we developed an algorithm to systematically generate 2D carbon crystals belonging to the family of graphdiynes (GDYs) and having different structures and sp/sp2 carbon ratio. We analyze how structural and topological effects can tune the relative stability and the electronic behavior, to propose a rationale for the development of new systems with tailored properties. A total of 26 structures have been generated, including the already known polymorphs such as α-, \b{eta}-…
Quantum anomalous Hall effect, with a trademark of dissipationless chiral edge states for electronics/spintronics transport applications, can be realized in materials with large spin-orbit coupling and strong intrinsic magnetization. After Haldane seminal proposal, several models have been presented to control/enhance the spin-orbit coupling and intrinsic magnetic exchange interaction. After brief introduction of Haldane model for spineless fermions, following three fundamental quantum anomalous Hall models are discussed in this perspective review: (i) low-energy effective four band model for …
We here investigated the thermal and mechanical behaviors of three-dimensional beta zeolite-templated carbon nanotube networks (BZCN). These networks are topologically generated by inserting carbon nanotubes (CNTs) into zeolite channels and connecting them using X-type junctions. We considered two cases, one with the tubes filling all zeolite channels (HD-BZCN) and the other with just partial filling (LD-BZCN). Fully atomistic reactive molecular dynamics (MD) simulations show that the networks exhibit high thermal stability (up to 1000 K). When compressed, the structures can withstand very lar…
Carbon is an extremely versatile element and carbon allotropes are very useful in all aspects of life and scientific research. T-carbon is a novel carbon allotrope with many appealing properties. Since the proposal of T-carbon, there has been a lot of intensive studies devoted to its physical, chemical, optical, magnetic, thermoelectrical and topological properties and possible applications in diverse areas in recent years. In this review, we provide a comprehensive review on the advances of the experiments, intriguing properties and various potential applications of T-carbon in energy storage…
The interplay between light and matter attracts tremendous interest for exploring novel topological quantum states and their phase transitions. Here we show by first-principles calculations and the Floquet theorem that a carbon allotrope bct-C$_{16}$, a typical nodal-line semimetal, exhibits exotic photoinduced Floquet mixed-Weyl semimetallic features. Under the irradiation of a linearly polarized light, bct-C$_{16}$ undergos a topological phase transition from a Driac nodal-line semimetal to a Weyl semimetal with two pairs of tunable Weyl points. With increasing the light intensity, left-hand…
Nodal chain is a typical topological phase in nodal line semimetals. Here, we propose a new topological phase -- interlocking nodal chains, in which two sets of nodal chains are interlocked each other. It includes one- (1D), two- (2D) and three-dimensional (3D) versions, which can be produced by a three-band model. The 2D and 3D interlocking nodal chains will evolve into some other phases, such as double concentric isolated (or intersecting) nodal rings, coexisting nodal chain and isolated (or intersecting) nodal rings. These phases exhibit diverse surface states and Landau levels, which impli…
As the aerospace industry becomes increasingly demanding for stronger lightweight materials, the ultra-strong carbon nanotube (CNT) composites with highly aligned CNT network structures could be the answer. In this work, a novel methodology applying topological data analysis (TDA) to the scanning electron microscope (SEM) images was developed to detect CNT orientation. The CNT bundle extensions in certain directions were summarized algebraically and expressed as visible barcodes. The barcodes were then calculated and converted into the total spread function $V(X,θ)$, from which the alignment f…
A new kind of three-dimensional carbon allotropes, termed carbon honeycomb (CHC), has recently been synthesized [PRL 116, 055501 (2016)]. Based on the experimental results, a family of graphene networks are constructed, and their electronic and phonon properties are calculated by using first principles methods. All networks are porous metal with two types of electron transport channels along the honeycomb axis and they are isolated from each other: one type of channels is originated from the orbital interactions of the carbon zigzag chains and is topologically protected, while the other type o…
Imidazolium cations are promising for anion exchange membranes, and electrochemical applications and gas capture. They can be chemically modified in many ways including halogenation. Halogenation possibilities of the imidazole ring constitute a particular interest. This work investigates fluorination and chlorination reactions of all symmetrically non-equivalent sites of the imidazolium cation. Halogenation of all carbon atoms is thermodynamically permitted. Out of these, the most favorable site is the first methylene group of the alkyl chain. In turn, the least favorable site is carbon of the…
Wires of sp-hybridized carbon atoms are attracting interest for both fundamental aspects of carbon science and for their appealing functional properties. The synthesis by physical vapor deposition has been reported to provide sp-rich carbon films but still needs to be further developed and understood in detail. Here the synthesis of carbon-atom wires (CAWs) has been achieved by nanosecond pulsed laser deposition (PLD) expoliting the strong out-of-equilibrium conditions occurring when the ablation plasma is confined in a background gas. Surface Enhnaced Raman scattering (SERS) spectra of deposi…
Tuning thermal transport in semiconductor nanostructures is of great significance for thermal management in information and power electronics. With excellent transport properties, such as ballistic transport, immunity to point defects and disorders, and forbidden backscattering, topological phonon surface states show remarkable potential in addressing this issue. Herein, topological phonon analyses are performed on hexagonal wurtzite GaN to check the topological characteristics of phonons. And other nitrides of the same family, i.e., AlN and AlGaN alloy, are also calculated from a topological …
Four sp3 carbon allotropes with six, eight, and 16 atoms per primitive cell have been derived using a combination of metadynamics simulations and topological scan. A chiral orthorhombic phase oC16 (C2221) was found to be harder than monoclinic M-carbon and shows excellent stability in the high-pressure range. A second orthorhombic phase of Cmmm symmetry, by \sim 0.028 eV/atom energetically lower than W-carbon, can be formed from graphite at \sim 9 GPa. In general, the mechanical response under pressure was found to depend on the structure topology, which reflects the way rings are formed from …
Topological superconductors (TSCs) have garnered significant research and industry attention in the past two decades. By hosting Majorana bound states which can be used as qubits that are robust against local perturbations, TSCs offer a promising platform toward (non-universal) topological quantum computation. However, there has been a scarcity of TSC candidates, and the experimental signatures that identify a TSC are often elusive. In this perspective, after a short review of the TSC basics and theories, we provide an overview of the TSC materials candidates, including natural compounds and s…
Several intramolecular junctions (IMJs) connecting two metallic (11, 8) and (9, 6) carbon nanotubes along their common axis have been realized by using a layer-divided technique to the nanotubes and introducing the topological defects. Atomic structure of each IMJ configuration is optimized with a combination of density-functional theory (DFT) and the universal force field (UFF) method, based upon which a four-orbital tight-binding calculation is made on its electronic properties. Different topological defect structures and their distributions on the IMJ interfaces have been found, showing dec…
Adsorption is one important way applied to water decontamination, where carbon is commonly used as highly effective absorbent. Carbon of different morphologies and structures normally demonstrate distinct capabilities to adsorption-typed decontaminations. Graphene oxide is regarded as the oxidative derivative of graphene, maintaining its 2D morphology-featuring structure while location-dependently immobilized with a large amount of various oxygen-involving functional moieties on both sides. Free-standing graphene oxide tends to fully unfold in water and behave in macromolecular-like Brownian m…
Carbon allotropes have a large family of materials with varieties of crystal structures and properties and can realize different topological phases. Using first principles calculations, we predict a new two-dimensional (2D) carbon allotrope, namely penta-octa-graphene, which consists of pentagonal and octagonal carbon rings. We find that penta-octa-graphene can host both type-I and type-II Dirac line nodes (DLNs). The band inversion between conduction and valence bands forms the type-I DLNs and the two highest valence bands form the type-II DLNs. We find that the type-I DLNs are robust to the …
Graphene as a two-dimensional (2D) topological Dirac semimetal has attracted much attention for its outstanding properties and potential applications. However, three-dimensional (3D) topological semimetals for carbon materials are still rare. Searching for such materials with salient physics has become a new direction for carbon research. Here, using first-principles calculations and tight-binding modeling, we study three types of 3D graphene networks whose properties inherit those of Dirac electrons in graphene. In the band structures of these materials, two flat Weyl surfaces appear in the B…
The quantal release of catecholamines from neuroendocrine cells is a key mechanism which has been investigated with a broad range of materials and devices, among which carbon-based materials such as carbon fibers, diamond-like carbon, carbon nanotubes and nanocrystalline diamond. In the present work we demonstrate that a MeV-ion-microbeam lithographic technique can be successfully employed for the fabrication of an all-carbon miniaturized cellular bio-sensor based on graphitic micro-channels embedded in a single-crystal diamond matrix. The device was functionally characterized for the in vitro…
